Find the indicated probabilities using the geometric...

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. An auto parts seller finds that 1 in every 100 parts sold is defective. Find the probability that (a) the first defective part is the tenth part sold, (b) the first defective part is the first, second, or third part sold, and (c) none of the first 10 parts sold are defective.

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.
An auto parts seller finds that 1 in every 100 parts sold is defective. Find the probability that (a) the first defective part is the tenth part sold, (b) the first defective part is the first, second, or third part sold, and (c) none of the first 10 parts sold are defective.

Key Concepts

Determining Unusual Events

An event is considered unusual if its probability is very low, commonly below a threshold such as 5%. Assessing whether an event is unusual helps in understanding how likely or unlikely an outcome is in the context of the expected behavior defined by the probability distributions.

Probability Calculations using Distributions

Probability calculations involve using the probability mass functions of the geometric or binomial distributions to determine the likelihood of certain outcomes. This requires identifying the correct parameters, such as the probability of success and the number of trials, then applying the formulas to compute the desired probabilities.

Geometric Distribution

The geometric distribution models the number of trials needed until the first success in a series of independent and identical Bernoulli trials. It is particularly useful when calculating the probability that the first occurrence of a specific event happens on a certain trial, with each trial having a constant probability of success.

Binomial Distribution

The binomial distribution describes the probability of obtaining a fixed number of successes in a fixed number of independent trials, each with the same probability of success. It is often used for scenarios where we need to determine the probability of a given number of events (either success or failure) occurring in a set sample size.

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